But I'm working with an imported STEP file of an assembly from another tool. SE seems to only let me move parts when I have the assembly open, not make synchronous edits involving multiple part surfaces at once.

The big difference I see in the demo video seems to be that the parts in the demo assembly seem to be shown in the Pathfinder as "Assembly Features" while in my imported STEP assembly case they are not. The imported STEP file brings in all the parts as "grounded" but I don't know if that's important here.